States of Matter
Liquefaction of Gases
Thomas Andrews obtained the first complete data on pressure-volume-temperature relations of a substance in both gaseous and liquid states for carbon dioxide. Later, it was found that real gases behave in the same manner as carbon dioxide.
It was observed that at high temperature, isotherms look like that of an ideal gas and the gas cannot be liquefied even at very high pressure. In this graph, point A represents gaseous state and point D represents liquid state. The points under the dome (B, C and E) represent existence of liquid and gaseous states in equilibrium.
Critical Temperature: The temperature at which liquid carbon dioxide appears for the first time is called critical temperature. It is 30.98° C. Volume of 1 M of gas at critical temperature is called critical volume and pressure at this temperature is called critical pressure. Critical pressure for carbon dioxide is 73 atm. Critical temperature, pressure and volume are called critical constants.
In this graph, horizontal lines represent the equilibrium between gaseous and liquid states. The steep lines represent the isotherms of liquid. It shows that a slight compression from volume V2 to V3 results in steep rise in pressure from p2 to p3. This shows that gases can be cooled below their critical temperature for liquefaction.
This study also shows that there is continuity between the gaseous and liquid state. To recognize this continuity, we use the term ‘fluid’ for gases and liquids.
If we fill an evacuated container partially with a liquid, a portion of liquid evaporates to fill the remaining volume of the container with vapor. Initially, the vapor pressure (of liquid) increases but becomes constant after some time. The equilibrium between vapor phase and liquid phase is established at this stage. At this stage, the vapor pressure is called equilibrium vapor pressure or saturated vapor pressure.
When we heat a liquid in an open container, liquid evaporates from the surface. When vapor pressure of liquid becomes equal to the external pressure (at a particular temperature), vaporization can take place throughout the bulk of the liquid. Vaporization throughout the bulk of the liquid is called boiling. The temperature at which vapor pressure of liquid becomes equal to the external pressure is called the boiling temperature or boiling point of the liquid. The boiling point at 1 atm pressure is called normal boiling point. The boiling temperature at 1 bar pressure is called standard boiling point. Standard boiling point of a liquid is slightly lower than normal boiling point because 1 bar is slightly less than 1 atm.
When a liquid is heated in a closed container, boiling does not occur. With adequate increase in temperature, a stage is reached when density of liquid and vapors becomes the same, and clear boundary between liquid and vapors disappears. This temperature is called critical temperature.
The force acting per unit length perpendicular to the line drawn on the surface of liquid is called surface tension. It is denoted by Greek letter gamma (Γ). The SI unit of surface tension is N m-1 and its dimension is kg s-2. When surface area is minimum, the liquid has the lowest energy state. Spherical shape satisfies this condition. Due to this, mercury drops or water drops have spherical shape.
Liquids tend to minimize their surface area. The molecules on the surface experience a net downward force and have more energy than the molecules in the bulk which do not experience any net force. So, liquids tend to have minimum number of molecules on their surface. The energy required to increase the surface area of the liquid by one unit is called surface energy. The dimensions of surface energy are J m-2.
Magnitude of surface tension depends on the attractive forces between molecules. Surface tension is large, when attractive forces are large. Surface tension decreases with increase in temperature because increase in temperature increases kinetic energy of molecules.
Layers of fluid slip past one another when a liquid flows. The resistance to flow due to internal friction between layers of fluid is called viscosity.
Laminar Flow: When a liquid flows over a surface, the layer of molecules in immediate contact of surface is stationary. The velocity of upper layer increases with increase in distance from the fixed layer. The type of flow in which there is regular gradation of velocity from one layer to the next is called laminar flow.
If the velocity of the layer at distance dz is changed by a value du then velocity gradient is `=(du)/(dz)`.
This force is proportional to the area of contact of layers and velocity of gradient.
F ∝ A
F ∝ `(du)/(dz)`
Or, F ∝ `A(du)/(dz)`
Here, Ƞ is the proportionality constant and is called the coefficient of viscosity. SI unit of viscosity coefficient is 1 N s m-2. A liquid with greater viscosity will flow more slowly than one with smaller viscosity.